simplify 2/3x-4/9y+x+y

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad \qquad m = -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-3}(x-\stackrel{x_1}{4})\implies y+1=-3(x-4) \\\\\\ y+1=-3x+12\implies \stackrel{\textit{slope-intercept form}}{y=-3x+11}[/tex]

does it pass through the origin?  well, we could draw it, or we can just check that, the origin is at 0,0, or namely when x = 0, y = 0, let's see if that's true, let's make x = 0, let's see what we get for "y".

y = -3(0) + 11 => y = 11

woops, no dice, y ≠ 0, so nope, doesn't pass through the origin.

Using the binomial distribution, it is found that there is a:

a) 0.3526 = 35.26% probability of rejecting a lot that is 3% defective.

b) 0.4295 = 42.95% probability of accepting a lot that is 4% defective.

For each device, there are only two possible outcomes, either it is defective, or it is not. The probability of a device being defective is independent of any other device, hence the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the sample has 100 units, hence [tex]n = 100[/tex].

Item a:

3% of the pieces are defective, hence [tex]p = 0.03[/tex].

The probability is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{100,0}.(0.03)^{0}.(0.97)^{100} = 0.0476[/tex]

[tex]P(X = 1) = C_{100,1}.(0.03)^{1}.(0.97)^{99} = 0.1471[/tex]

[tex]P(X = 2) = C_{100,2}.(0.03)^{2}.(0.97)^{98} = 0.2252[/tex]

[tex]P(X = 3) = C_{100,3}.(0.03)^{3}.(0.97)^{97} = 0.2275[/tex]

Then:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0476 + 0.1471 + 0.2252 + 0.2275 = 0.6474[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6474 = 0.3526[/tex]

0.3526 = 35.26% probability of rejecting a lot that is 3% defective.

Item b:

4% of the pieces are defective, hence [tex]p = 0.04[/tex].

Lot is accepted if less than 4 units are defective, hence:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

[tex]P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169[/tex]

[tex]P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703[/tex]

[tex]P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450[/tex]

[tex]P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973[/tex]

Then:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0169 + 0.0703 + 0.1450 + 0.1973 = 0.4295[/tex]

0.4295 = 42.95% probability of accepting a lot that is 4% defective.

A similar problem is given at https://brainly.com/question/24863377

Answer:

The answer is 3

Step-by-step explanation:

I am sure.

Answer: i think it is 3

Step-by-step explanation:

Answer:

i thank it h

Step-by-step explanation:

Answer:

Well your answer is (F)

Step-by-step explanation:

?

Step-by-step explanation:

The lines or plains which contain R:

Answer:

650 students are spanish.

Step-by-step explanation:

just say 1,000 people = 100%

then 650 students would = 65%

Hope I helped

Answer: the difference if that 5.4 is not a negative number they are relatied because it takes them both 5.4 ,3 moves to get to 0

Step-by-step explanation:

Answer:

. Kelsey takes out a loan for $6000 to start a business after high school. The bank charges her 8% simple interest for the loan. Term is five years. After 5 years , what will the balance be for the repayment of this loan? (round to nearest cent)

Step-by-step explanation:

Answer:

67 i thing so if it wrong sorry and ill answer  it again ight

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

3^3+14*y-(25*y-13)-(y+7*y-9*y)=0

Equation at the end of step 1

((3³ + 14y) - (25y - 13)) - -y = 0

Pull out like factors :

40 - 10y = -10 • (y - 4)

Equation at the end of step3:

-10 • (y - 4) = 0

STEP4:

Equations which are never true:

Solve : -10 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

Solve : y-4 = 0

Add 4 to both sides of the equation :

y = 4

[tex]\sin \theta -1 =0\\\\\ \implies \sin \theta = 1\\\\ \implies \theta = \dfrac{\pi}2 + 2\pi n\\\\\text{For n =0,}\\\\\theta = \dfrac{\pi}2[/tex]

Answer:

x=-52

1/3x-2/3=-18

multiply both sides by 3

x-2=-54

x=-54+2

x=-52

Answer:

the slope is -2/5

Step-by-step explanation:

Solve for y.

2x + 5y + 1 = 0

5y = -2x - 1

y = -2/5 x - 1/5

Compare to

y = mx + b, where m is the slope.

m = -2/5

Answer: the slope is -2/5

Answer:

[tex]25\frac{3}{2} =26.5[/tex]

Step-by-step explanation:

This mixed number can be separated into 25 and [tex]\frac{3}{2}[/tex]. Convert the fraction to a decimal by plugging it into a calculator, then add 25.

If you meant what whole number is equivalent, that does not exist.

It is 1.39 standard devaitions away from the mean.

Since the mean x = 51.84 inches and the standard deviation, σ = 8.05 inches.

The amount of rainfall last year was X = 63 inches.

The difference between X and the mean x is d = X - x

= 63 - 51.84 in

= 11.16 in

To find the number of standard devaitions X is from the mean, n, we divide d by the standard deviation,σ.

So, n = d/σ

= 11.16 in/8.05 in

= 1.39

So, it is 1.39 standard devaitions away from the mean.

Learn more about number of standard deviations here:

https://brainly.com/question/24254824

Answer:

3.2%

Step-by-step explanation:

2 / 63 = 0.031746031746

0.031746031746 x 100 = 3.1746031746 and round

Answer:

675$

Step-by-step explanation:

got it right

Answer:

f(X)= 4 and g(X)= 49 are the answers!

Answer:

f(6) = -8

g(-3) = 49

Step-by-step explanation:

So when observing a function we have to remember that the desired input value is correspondent to the function. So when looking at the first function of:

f(x) = -2x+4

we can see that we are trying to find f(6) meaning all of the values of x are 6 in the equation. When plugging in the value of x into the equation then we have:

f(6) = -2(6)+4

the next step would be to simplify. -2*6 = -12 and -12+4=-8 and thus:

f(6) = -8

Now the steps are the same with g(-3) except with the other function:

g(x) = -2x^3-5

g(-3) = -2(-3)^3-5

g(-3) = 49

Hey where are the questions?

rhombus opposite sides are equal.

So, CD = 15

Answer:

A' 2,2

B' 3, -1

C' -1,0

Step-by-step explanation:

Because you're translating it by -2, 3, you're basically subtracting 2 from the x value and adding 3 to the y value.

A = 4, -1

A' = 2, 2

B = 5, -4

B' = 3, -1

C = 1, -3

C' = -1, 0

Answer:

b) quotient

Step-by-step explanation:

divisor is the number/value you are dividing with.

A remainder is a number that remains after you divide.

A factor is a number that can divide into a number or numbers without leaving a remainder

Answer:2 muffins

Step-by-step explanation: First you have to see how many muffins he baked. 12x4 = 48 thus giving us the amount of muffins he baked. 48 muffins. If each student gets the same amount of muffins 48/24 = 2.

So each person would get 2 muffins.

Hope this helps :)

[tex]g(x) = 4 |x| = x = 0[/tex]

Answer:

A.

Step-by-step explanation:

You can see that the rate of change of function A is 3. because that's the slope (M) in y=mx+b

5 is slope for B because unit rate is 5 ( 1 to 3 change is +10 so unit rate is 5)

Each digit can be one of {1, 3, 5, 7, 9}, so there are 5 choices for each. Then there are 5•5•5 = 5³ = 125 integers containing only odd digits, which means they make of 125/900 ≈ 14% of them.

The assumptions required for making inference about a population using sample data include ;

Learn more : https://brainly.com/question/25609474

Step-by-step explanation:

∵ MP is a straight line.

∴ ∠MNQ + ∠PNQ = 180°

[tex](3y + 8)° + (3y + 22)° = 180° \\ 3y + 8 + 3y + 22 = 180 \\ 6y + 30 = 180 \\ 6y = 150 \\ y = 25[/tex]

∵ MP is a straight line.

∴ ∠MNR + ∠PNR = 180°

[tex](2x + 5)° + (3x - 55)° = 180° \\ 2x + 5 + 3x - 55 = 180 \\ 5x - 50 = 180 \\ 5x = 230 \\ x = 46[/tex]